For the slaw, squeeze excess liquid out of kimchee. Take the wringed ball of kimchee and thinly slice it (so it looks like cole slaw). In a bowl, combine kimchee with the sugar, sesame oil and sesame seeds. Set aside.

Grill patties about 5-6 minutes per side or until desired doneness. As patties rest after being grilled, prepare fried egg: In medium skillet, heat 2 tablespoons vegetable oil over medium-high heat. Crack 3 eggs, sunny side up (try to keep them separate). Carefully break yolk and then flip. Repeat with remaining 3 eggs and 2 tablespoons of oil.

Toast buns 1-2 minutes on remaining heat of grill. Place patty on bun, top with a fried egg and then finish it off with a spoonful of kimchee slaw.